We present in this paper some results for solving the Quadratic Eigenvalue Complementarity Problem (QEiCP) by using DC(Difference of Convex functions) programming approaches. Two equivalent Nonconvex Polynomial Programming (NLP) formulations of QEiCP are introduced. We focus on the construction of the DC programming formulations of the QEiCP from these NLPs. The corresponding numerical solution algorithms based on the classical DC Algorithm (DCA) are also discussed.